In an optical communication system such as a dense wave division multiplexing system, an arrayed waveguide grating (AWG) is a key optical device to carry out multiplexing and de-multiplexing of a plurality of optical signals to thereby increase capacity of the optical communication system. The AWG is an optical device based on a planar optical waveguide, and it generally includes an input waveguide, an input slab waveguide, arrayed waveguides, an output slab waveguide, and output waveguides. Among the arrayed waveguides, every two adjacent waveguides have a constant length difference. A plurality of optical signals with different wavelengths enter into the AWG at a same input port and are diffracted while passing through the input slab waveguide, thereby distributing optical power to each of the arrayed waveguides. Due to the length difference, the arrayed waveguides will cause different transmission phase delays, which coherently superimpose each other in the output slab waveguide so that lights of different wavelengths are outputted to different output ports, thereby de-multiplexing the optical signals. On the contrary, if a plurality of optical signals enter into the AWG from different output ports, they will be multiplexed at the input port.
The dense wave division multiplexing system requires the multiplexing/de-multiplexing device has a stable center wavelength that is controlled within a certain proportion of the channel spacing. For example, in a wave division multiplexing system with 100 GHz channel spacing, accuracy of the center wavelength often needs to be controlled within ±(5%-10%) of the channel spacing, i.e., ±(40-80) pm. For a denser wave division multiplexing system such as 50G and 25G systems, a higher accuracy of the center wavelength is required, which may reach ±40 pm and ±20 pm respectively or even higher, as shown in the following table.
Accuracy of Accuracy of Accuracy of central wavelength central wavelength central wavelength Channel(acceptable,(appropriate,(optimal,spacing±10%, pm)±5%, pm)±2.5%, pm)100 GHz±80±40±20 50 GHz±40±20±10 25 GHz±20±10±5 
At present, the commercially available AWG chips are generally silicon-based planar optical waveguide devices, the center wavelength of which varies relatively greatly with ambient temperature at a rate of about 12 pm/° C. Then, at the operation ambient temperature of the wave division multiplexing system (−5° C. to 65° C.), a drifting quantity of the center wavelength of the AWG chip may be up to about 800 pm, which obviously goes beyond the system requirement. Therefore, the center wavelength of the AWG chip needs to be controlled to make sure that the AWG chip works well at the operation ambient temperature.
An athermal AWG (AAWG) can effectively control the problem of the center wavelength of the AWG chip drifting with the temperature, and it is a purely passive device that does not consume electric power, so it has attracted lots of attention. Patent CN101019053B (PCT/US2004/014084, May 5, 2004) discloses a conventional AAWG, as shown in FIG. 10, which includes a base, and a chip attached to the base. A slab waveguide of the chip is divided into two parts, and an actuator 301 of the base drives a hinge 202 to move so that waveguides of the chip on the base move with respect to each other to compensate variation of the center wavelength of the AWG chip with the temperature.
Formula 1 shows a relationship between a relative displacement dx of the separated slab waveguide of the AWG and a temperature variation dT:
                              dx          dT                =                                            dx                              d                ⁢                                                                  ⁢                λ                                      ⁢                                          d                ⁢                                                                  ⁢                λ                            dT                                =                      R            ⁢                          m                                                n                  s                                ⁢                d                                      ⁢                                          n                g                                            n                c                                      ⁢                                          d                ⁢                                                                  ⁢                λ                            dT                                                          Formula        ⁢                                  ⁢        1            
Here, ns and nc are effective refractive indexes of the input/output slab waveguides and the arrayed waveguides of the AWG respectively, ng is a group refractive index, d is a pitch of adjacent arrayed waveguides on a Rowland circle, m is a diffraction order, R is a focal length of the Rowland circle, and dλ is a variation value of the center wavelength of the AWG.
Assuming an effective length L and a linear expansion coefficient ∂ of the actuator 301, a relative displacement caused by thermal expansion of the actuator 301 is as follows:dx=k×L×∂×dT  Formula 2
Here, k is a leverage factor between a displacement of the actuator 301 and a relative displacement of a first region and a second region of the base.
The following relationship can be obtained by combining the Formulae 1 and 2:
                                          d            ⁢                                                  ⁢            λ                    dT                =                                            k              ×              L              ×              ∂                        R                    ⁢                                                    n                s                            ⁢              d                        m                    ⁢                                    n              c                                      n              g                                                          Formula        ⁢                                  ⁢        3            
It can be seen from the Formula 3 that in the technical solution of the Patent, the variation value of the center wavelength of the AWG linearly depends on the variation value of the temperature T.
However, the variation value of the center wavelength λ of an AWG chip may not have a simple linear relationship with the temperature T, but a nonlinear relationship as shown in the following Formula 4:dλ=a×dT2+b×dT+c  Formula 4
The conventional solution can only compensate the first-order item of the center wavelength variation with the temperature, but cannot compensate the second-order item. FIG. 11 shows dependence of wavelength variation on temperature after linear compensation, which is a parabola curve indicating a residual wavelength/temperature nonlinear effect.
With continuous development of Wavelength Division Multiplexing-Passive Optical Network (WDM-PON) in recent years, the AWG are used in both indoor and outdoor applications, and the operation ambient temperature extends from −5° C.˜65° C. to −40° C.˜85° C. The drifting quantity of the center wavelength with the temperature becomes larger, and the requirement to the wavelength control becomes higher. it can be seen from FIG. 11 that when the operation ambient temperature extends from −5° C.˜65° C. to −40° C.˜85° C., the accuracy of the center wavelength would increase from 40 pm to 70 pm, which may go beyond the requirement.
The conventional solution for first-order linear compensation cannot meet the requirements for application of a broader operation temperature range or a denser wave division multiplexing system. There is a need for a nonlinear compensation solution to control the center wavelength of the AAWG more accurately.
Furukawa and Gemfire companies have proposed solutions for nonlinear compensation. For example, U.S. Pat. No. 7,539,368B2 discloses a method of segmental temperature compensation in which the operation temperature range is divided into 3 segments, each of which adopts a different linear compensation to reduce the second-order temperature effect. In this solution, the chip is divided into two parts, and the two parts are free to move with respect to each other. In such a case, either one of the two parts may easily slide and thus be dislocated with respect to the other, which may cause instability of wavelength accuracy and insertion loss.
U.S. Pat. No. 7,689,072B2 discloses a method of nonlinear temperature compensation by filling two different compensating materials, one of which is filled for linear compensation, and the other is added for the second-order nonlinear compensation. In this solution, a plurality of slots are directly added in the light path of the chip, and the compensating materials are filled in the slots. It is easy to manufacture and realize miniaturization. However, the two different compensating materials may interfere with each other, and the second-order compensation effect is not obvious.
So, it is still a problem to propose a solution to solve the nonlinear effect and to ensure stability and reliability of the optical device.